EP3384278B1 - Method and system for generating a theoretical backscattered intensity profile of a polycrystalline material with known crystal orientation - Google Patents

Description

TECHNICAL AREA

The present invention relates to the general technical field of the characterization of a sample made of polycrystalline material. These materials are for example ceramics, metals, etc.

PRESENTATION OF PRIOR ART

A poly-crystalline material is a solid material made up of a plurality of small crystals - called "grains" - of varying sizes and crystal orientations, as opposed to a monocrystalline material made up of a single crystal and an amorphous material without long distance order.

Most materials (in the field of microelectronics, new energies, alloys, ceramics, minerals) are composed of crystals of different size, shape and structure.

The anisotropy of poly-crystalline materials has multiple impacts on their characteristics, in particular on their mechanical properties (resistance to cracking, breaking, etc.) or even on their electrical properties.

Knowledge of the crystalline orientation of the grains composing a polycrystalline material is therefore very important.

• la réception d'une série d'images de l'échantillon acquises par un dispositif d'acquisition, les images étant acquises pour des géométries d'éclairage de l'échantillon différentes, chaque image incluant des pixels représentant des intensités de points de l'échantillon pour une géométrie d'éclairage respective,
• l'estimation d'au moins un profil d'intensités pour au moins un point considéré du matériau à partir de la série d'images, chaque profil d'intensités représentant l'intensité associée au point considéré en fonction de la géométrie d'éclairage,
• la détermination d'une orientation cristalline pour chaque point considéré du matériau en comparant le profil d'intensités associé audit point considéré à des signatures théoriques de profils d'intensités d'orientations cristallines connues contenus dans une base de données.

The document WO2015113898 describes a method for mapping the crystalline orientations of a sample made of polycrystalline material, the method comprising:

• receiving a series of images of the sample acquired by an acquisition device, the images being acquired for different illumination geometries of the sample, each image including pixels representing point intensities of the sample for a respective lighting geometry,
• estimating at least one intensity profile for at least one point considered on the material from the series of images, each intensity profile representing the intensity associated with the point considered as a function of the lighting geometry ,
• determining a crystal orientation for each point considered of the material by comparing the intensity profile associated with said point considered with theoretical signatures of intensity profiles of known crystal orientations contained in a database.

This process - based on the comparison of an estimated intensity profile to theoretical signatures - is very effective. It allows characterization of the crystal orientations of a poly-crystalline sample which is simple, quick and inexpensive to implement.

Different methods are known for obtaining the theoretical signatures contained in the database.

A first method consists of experimentally measuring the intensity of a crystal whose orientation is known for different acquisition geometries. However, this method is very time consuming. For example the document XP055266074 by C. LANGLOIS ET AL: “Crystal orientation mapping via ion channeling: An alternative to EBSD”, ULTRAMICROSCOPY, vol. 157, June 5, 2015, pages 65-72 , describes a method in which theoretical signatures are calculated for each point of a sample using an experimental profile, information on the Euler angles at the point considered (obtained by EBSD) and information on the crystal system (ie cubic , orthorhombic, hexagonal, etc.) of the sample (see XP055266074, page 67, right column, paragraph 2).

Another method consists of estimating theoretical signatures from three-dimensional (3D) modeling. For example, the document XP055176507 by VASILISA VELIGURA ET AL: "Channeling in helium ion microscopy: Mapping of crystal orientation", BEILSTEIN JOURNAL OF NANOTECHNOLOGY, vol. 3, July 10, 2012 (2012-07-10), pages 501-506 describes a method for generating theoretical signatures computationally.

1. i) création dans un logiciel de modélisation 3D, d'un volume composé de mailles élémentaires, chaque maille incluant des atomes constituant la structure d'un cristal pour lequel on souhaite calculer une signature théorique,
2. ii) projection des atomes du cristal dans un plan et calcul de l'intensité totale de la projection (en pratique, les atomes représentés par des sphères de couleur blanche sont projetés dans un plan de couleur noir et l'intensité totale de la projection est déduite de la quantité de noir dans le plan),
3. iii) répétition de l'étape ii) pour différentes orientations angulaires du cube. Pour certaines orientations (cf. figure 1a), il est aisé de distinguer les alignements d'atomes en analysant leurs projections 11 dans le plan de projection 21.

This method includes the following steps:

1. i) creation in 3D modeling software, of a volume composed of elementary cells, each cell including atoms constituting the structure of a crystal for which we wish to calculate a theoretical signature,
2. ii) projection of the atoms of the crystal in a plane and calculation of the total intensity of the projection (in practice, the atoms represented by white colored spheres are projected into a black colored plane and the total intensity of the projection is deducted from the quantity of black in the plane),
3. iii) repetition of step ii) for different angular orientations of the cube. For certain directions (cf. figure 1a ), it is easy to distinguish the alignments of atoms by analyzing their projections 11 in the projection plane 21.

However, a disadvantage of this method is that it can induce ambiguities. In particular and as illustrated in figures 1b and 1c , the intensities calculated from projections 12, 13 of two very different orientations can turn out to be almost identical. Furthermore, for certain orientations, the intensity profiles calculated by this method can present numerous artifacts compared to the experimental intensity profiles for the same crystal according to the same orientations.

It can then prove difficult to define the orientation of the crystal by comparing an experimentally measured intensity profile to a calculated intensity profile.

As for the document XP020247229 by ROSCA D ET AL: "Area-preserving projections from hexagonal and triangular domains to the sphere and applications to electron back-scatter diffraction pattern simulations", MODELING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING, IOP PUBLISHING, BRISTOL, GB, vol. 21, no. 5, June 11, 2013, page 55021 , it describes an equal area mapping technique based on the Lambert projection method distorting the crystal structure.

An aim of the present invention is to propose a method for calculating theoretical signatures making it possible to overcome at least one of the drawbacks of the aforementioned methods.

SUMMARY OF THE INVENTION

To this end, the invention proposes a method for creating a theoretical signature of a sample of crystalline material, the theoretical signature corresponding to a curve of theoretical backscattered intensities as a function of acquisition geometries according to claim 1.

• la structure tridimensionnelle peut être sphérique,
• l'étape de définition peut consister, pour un atome donné de la structure, à attribuer une valeur de niveau de gris à chaque atome en fonction de la distance entre ledit atome donné, la valeur de niveau de gris attribuée étant calculé à partir d'une fonction de décroissance de la forme suivante : $$N\left(d\right)=\alpha .d^{\beta }$$
  

Preferred but non-limiting aspects of the system according to the invention are the following:

• the three-dimensional structure can be spherical,
• the definition step may consist, for a given atom of the structure, of assigning a gray level value to each atom as a function of the distance between said given atom, the assigned gray level value being calculated from a decay function of the following form: $$\mathrm{NOT}\left(d\right)=\alpha .d^{\beta }$$
  

• ∘ N(d) : le niveau de gris à attribuer à l'atome
• o d : la distance entre l'atome et le plan de projection,
• o α et β des coefficients fixes

• l'étape de calcul de la projection peut comprendre l'attribution à chaque pixel de l'image de projection :
  • o de la valeur 0 si aucun atome n'est traversé par la direction de projection,
  • ∘ de la valeur associée à l'atome le plus proche du plan de projection si au moins un atome est traversé par la direction de projection,
• l'étape d'estimation de l'intensité peut comprendre l'application d'une fonction polynomiale aux valeurs de niveau de gris des pixels de l'image de projection,
• l'étape d'estimation de l'intensité comprend les sous-étapes consistant à :
  • o sélectionner une région de l'image de projection,
  • o sommer les valeurs niveau de gris des pixels de la région sélectionnée, et
  • ∘ diviser la somme obtenue par le nombre de pixels de la région sélectionnée.

• l'étape de modélisation comprend les sous-étapes consistant à :
  • ∘ produire un motif atomique élémentaire composé d'atomes, notamment à partir d'un logiciel de modélisation tridimensionnel,
  • ∘ répéter le motif atomique (notamment une pluralité de fois) selon au moins une (notamment chacune) des trois dimensions de l'espace pour générer un squelette cristallin tridimensionnel,
  • ∘ former une structure tridimensionnelle atomique à partir du squelette cristallin tridimensionnel.

With :

• ∘ N(d): the gray level to attribute to the atom
• od: the distance between the atom and the projection plane,
• o α and β fixed coefficients

• the projection calculation step may include the allocation to each pixel of the projection image:
  • o the value 0 if no atom is crossed by the direction of projection,
  • ∘ of the value associated with the atom closest to the projection plane if at least one atom is crossed by the projection direction,
• the intensity estimation step may include the application of a polynomial function to the gray level values of the pixels of the projection image,
• the intensity estimation step comprises the sub-steps consisting of:
  • o select a region of the projection image,
  • o sum the gray level values of the pixels of the selected region, and
  • ∘ divide the sum obtained by the number of pixels in the selected region.

• the modeling step includes the sub-steps consisting of:
  • ∘ produce an elementary atomic pattern composed of atoms, in particular from three-dimensional modeling software,
  • ∘ repeat the atomic pattern (in particular a plurality of times) according to at least one (in particular each) of the three dimensions of space to generate a three-dimensional crystal skeleton,
  • ∘ form a three-dimensional atomic structure from the three-dimensional crystal skeleton.

The invention also relates to a computer program product according to claim 8 comprising programming code instructions for executing the steps of the method described above when said program is executed on a computer.

BRIEF DESCRIPTION OF THE FIGURES

• les figures 1a, 1b, et 1c illustrent les projections dans un plan d'un cristal selon trois orientations différentes,
• la figure 2 illustre un exemple de procédé de génération de signatures théoriques
• les figures 3a, 3b, 4a, 4b illustrent des vues en coupes d'une structure cristalline cubique pour différentes orientations par rapport à un plan de projection.
• la figure 5 est une image en niveaux de gris représentant une projection dans un plan de projection des atomes d'une structure cristalline.

Other characteristics, aims and advantages of the present invention will emerge further from the description which follows, which is purely illustrative and not limiting and must be read with reference to the appended drawings in which:

• THE figures 1a, 1b, and 1c illustrate the projections in a plane of a crystal in three different orientations,
• there figure 2 illustrates an example of a method for generating theoretical signatures
• THE figures 3a, 3b, 4a, 4b illustrate cross-sectional views of a cubic crystal structure for different orientations relative to a projection plane.
• there figure 5 is a grayscale image representing a projection in a projection plane of the atoms of a crystal structure.

DETAILED DESCRIPTION

We will now describe in more detail a method and a system for generating theoretical signatures for mapping the crystalline orientations of a sample of polycrystalline material with reference to the figures. In these different figures, the equivalent elements bear the same numerical references.

1. General

The objective of the method described below is to allow the creation of theoretical signatures obtained by calculation using three-dimensional modeling.

A theoretical signature is a curve representing a theoretical intensity as a function of an acquisition geometry for a material of known crystallographic orientation.

The theoretical signatures can be used to determine the crystalline orientation of each grain of a sample of polycrystalline material, by comparing said theoretical signatures with a profile of measured intensities.

An intensity profile associated with a point of the sample is a curve representing the intensity measured by a detector p as a function of an acquisition geometry. Such an intensity profile is obtained by acquiring a series of images of the sample using an acquisition device for different acquisition geometries.

The acquisition geometry corresponds for each image to the relative position of the sample with respect to an acquisition device used to measure the intensity of the sample.

The purpose of the method according to the invention is to generate a theoretical signature (or theoretical profile) for a given material and a given crystal orientation as would be produced by its experimental measurement.

To understand the different characteristics of the process for creating theoretical signatures, we will briefly recall the stages of experimental measurement of an intensity profile of a point on the surface of a material to be analyzed.

Indeed, the technical choices made as part of the process of creating theoretical signatures are directly related to the physical phenomena governing the acquisition and processing of experimental data.

2. Brief reminder of the principles relating to the experimental measurement of intensity profiles

• l'acquisition d'une série d'images de l'échantillon pour différentes géométries d'acquisition, et
• le traitement des images acquises pour en déduire un profil d'intensités en chaque point de l'échantillon.

A method for experimentally measuring the intensity profile of a polycrystalline sample includes two main steps:

• acquiring a series of images of the sample for different acquisition geometries, and
• processing the acquired images to deduce an intensity profile at each point of the sample.

2.1. Acquisition

• émettre un faisceau de particules chargées à partir d'une source, et pour
• collecter un signal en provenance de l'échantillon sur un détecteur.

The acquisition of a series of images is implemented in an acquisition device adapted for:

• emit a beam of charged particles from a source, and to
• collect a signal from the sample on a detector.

The acquisition device is for example a scanning electron microscope or a focused ion probe. The principle of acquiring an image using the acquisition device is as follows.

The source generates a primary beam of charged particles which impacts the surface of a sample. As a result, a signal (e.g. secondary and backscattered charged particles) is emitted from the sample surface and the respective trajectories of the particles constituting the signal follow in reverse the original direction of the primary beam, which is perpendicular to the surface. of the sample (known as the axial direction) and with angles diverging from it.

Said particles are collected by the detector, placed above the sample. The detector generates a signal from the collected particles. This signal is processed to create a pixel of an image of the material.

Each image is obtained for a respective acquisition geometry (ie relative position of the source and the detector relative to the sample). This image is representative of the intensities measured by the detector during the interaction of the beam of particles charged with the atoms of the sample. These measured intensities vary depending on the orientation of the crystal lattice relative to the beam, the material and the experimental conditions (acquisition geometry in particular).

To obtain a series of images, we repeat the operations described above for different acquisition geometries.

2.2. Treatment

The processing of the series of images is implemented in a processing device adapted to calculate an intensity profile at each point on the surface of the material from the series of images.

Each acquired image is composed of pixels whose gray levels - between 0 and 255 - are representative of electronic intensities received by the detector.

Each pixel is representative of the intensity of a corresponding point of the sample, this intensity depending on the crystal orientation at the point considered and the angle which defines the acquisition geometry (i.e. positions of the source and detector compared to the sample).

Thus, the intensity of the same point of the sample varies in the images of the series of images.

For each point of the sample, the homologous pixels of the different images are grouped, and their values are reported in a graph representing the intensity of the point of the sample as a function of the acquisition geometry.

3. Process

• une phase de modélisation 10 tridimensionnelle au niveau atomique d'un échantillon du matériau,
• une phase de positionnement 20 du modèle tridimensionnel par rapport à un plan perpendiculaire au faisceau de particules chargées, ledit plan - appelé dans la suite « plan de projection » - représentant la position du détecteur dans le dispositif d'acquisition,
• une phase de définition 30 pour chaque atome 24 du modèle tridimensionnel d'un niveau d'interaction théorique avec le faisceau de particules chargées en fonction de la modélisation,
• une phase de projection orthogonale 40 du modèle tridimensionnel sur un plan de projection en tenant compte des niveaux d'interaction et de la visibilité des atomes du modèle,
• une phase d'évaluation 50 de l'intensité théorique par analyse de la projection orthogonale produite.

We will now describe in more detail an example of a method for generating theoretical signatures. The process may include the following main phases:

• a three-dimensional modeling phase 10 at the atomic level of a sample of the material,
• a positioning phase 20 of the three-dimensional model relative to a plane perpendicular to the beam of charged particles, said plane - hereinafter called "projection plane" - representing the position of the detector in the acquisition device,
• a definition phase 30 for each atom 24 of the three-dimensional model of a theoretical level of interaction with the beam of charged particles according to the modeling,
• an orthogonal projection phase 40 of the three-dimensional model on a projection plane taking into account the interaction levels and the visibility of the atoms of the model,
• a phase of evaluation 50 of the theoretical intensity by analysis of the orthogonal projection produced.

3.1. Three-dimensional modeling

Phase 10 of the process consists of modeling the atomic skeleton of the polycrystalline material for which it is desired to generate a theoretical signature. Unlike the method according to the present invention, the method described in document XP055266074 does not include a modeling step to calculate theoretical signatures. Indeed in XP055266074, the theoretical signatures are calculated using experimental profiles. Modeling the atomic skeleton of the polycrystalline material for which we wish to generate a theoretical signature makes it possible to limit the costs and time associated with the generation of theoretical signatures. In a first step, an elementary atomic pattern composed of 24 atoms - or " crystal lattice" - is produced using three-dimensional modeling software. Each atom 24 is represented by a sphere, the sizes and positions of the different atoms 24 being determined so as to respect theoretical and experimental data relating to the crystallography of the material.

The elementary pattern is then repeated periodically a plurality of times in the three dimensions of space to form a three-dimensional crystal skeleton representative of the material for which it is desired to generate the theoretical signature. The crystal skeletons thus obtained can have different shapes, such as a parallelepiped, cubic, hexagonal shape, etc.

A step of the modeling consists of selecting the atoms 24 of the skeleton contained in a selection volume having a central symmetry of revolution such as a sphere. This makes it possible to standardize the depth of analysis of the material considered. More precisely, this makes it possible to make the depth of analysis of the material independent of the acquisition geometry.

Indeed, in order to construct a theoretical signature of the intensities of a crystalline material of known crystalline orientation, it is necessary to determine the theoretical intensity level of each atom 24 for different acquisition geometries.

To do this, it is preferable that the analysis depth (i.e. distance between the projection plane 21 and the atom 24 of the material furthest from said plane in a projection direction 23) remains approximately constant whatever the geometry d 'acquisition.

• une première géométrie d'acquisition (figure 3a) et
• une deuxième géométrie d'acquisition (figure 3b) correspondant à une rotation du squelette d'un angle de 45° par rapport à la première géométrie d'acquisition.

This is not the case when the skeleton is, for example, cubic. Indeed, during a rotation of a cubic crystal skeleton, the analysis depth considered changes. This is illustrated in Figure 3 where the same cubic crystal skeleton is represented for:

• a first acquisition geometry ( figure 3a ) And
• a second acquisition geometry ( figure 3b ) corresponding to a rotation of the skeleton by an angle of 45° relative to the first acquisition geometry.

In the case of the figure 3a , the analysis depth is constant over the entire projection. In the case of the figure 3b , the analysis depth varies between the center and the periphery of the cubic crystal skeleton.

The fact that the analysis depth is different between the first and second acquisition geometries introduces mathematical instability into the estimation of the intensity for each of these acquisition geometries.

To make the depth of analysis independent of the acquisition geometry of the crystal structure, the inventors propose to consider (during the following phases of the process) only the atoms 24 contained in a sphere 22 inscribed in the crystal skeleton, as illustrated to figures 4a and 4b .

This is why the modeling phase can include a step consisting of forming a crystal structure of interest from the crystal skeleton, the structure comprising at least one crystal unit and being contained in a volume having a symmetry of revolution so that the distance between a center of the structure and the atoms 24 arranged at the periphery of the structure is substantially constant.

• la paroi de la plus petite sphère dans laquelle ladite structure est inscrite, et
• chaque atome 24 de la périphérie de la structure

est inférieure à deux fois la distance entre deux atomes adjacents de la structure.We thus obtain a spherical three-dimensional atomic structure. In the context of the present invention, the term “ spherical ” atomic structure means a structure in which the distance between:

• the wall of the smallest sphere in which said structure is inscribed, and
• each atom 24 of the periphery of the structure

is less than twice the distance between two adjacent atoms of the structure.

Thus, whatever the acquisition geometry chosen, the depth remains approximately the same from one acquisition geometry to another (cf. figures 4a and 4b ).

Once the modeling phase is completed, the following phases of the process (i.e. phases of positioning, definition of an interaction level, projection and estimation) are iterated for different positions of the crystal structure relative to the plane of projection 21.

The positioning phase consists of arranging the modeled three-dimensional structure relative to the projection plane 21 according to the desired acquisition geometry. This classic phase itself will not be described in more detail below.

3.2. Interaction Levels

Another phase of the method consists, for each atom 24 of the structure, in defining a theoretical level of interaction between said atom 24 and the beam of charged particles, this level of interaction depending on the position of the atom 24 relative to to the projection plane (and therefore the positioning of the structure).

This phase makes it possible to limit the risks of saturation during the subsequent phase of projection of the structure onto the projection plane 21.

The saturation phenomenon can be explained as follows with reference to figures 1a to 1c .

For certain acquisition geometries as illustrated in figure 1a , it is easy to distinguish the alignments of atoms 24 by analyzing the projection of the spherical crystal structure on the projection plane 21. On the other hand, when the atoms 24 do not present a marked alignment, the analysis becomes more difficult.

Indeed, the projection of the structure according to two very different acquisition geometries but not presenting any marked alignment can be almost identical because it is totally saturated, particularly at the center of the structure where the analysis depth is greatest (see . figures 1b and 1c ).

However, the level of intensity observed experimentally would be very different for these two acquisition geometries. This phenomenon is all the more marked as the number of atoms 24 in the structure increases. In the limiting case of a very large number of atoms 24, the projection would be totally saturated from the slightest misalignment.

This is counterintuitive and problematic because modeling a larger number of atoms 24 should increase the accuracy of the theoretical model and not degrade it.

In order to avoid this saturation phenomenon, the inventors propose to define for each atom 24 of the three-dimensional structure a level of interaction which is a decreasing function of the distance of the atom from the projection plane 21.

From a physical point of view, this function represents the probability of interaction of the beam of charged particles emitted by the source with the atom 24 considered. Thus, the atoms 24 closest to the projection plane 21 are considered to interact strongly with the beam of charged particles, and produce a high intensity. In other words, in the case of an ion beam for example, the atoms 24 close to the projection plane 21 (and therefore corresponding to atoms 24 of the material close to the source and the detector) are considered to produce a large quantity of secondary and backscattered charged particles. Conversely, the atoms 24 in depth (i.e. very far from the projection plane 21 corresponding to the plane containing the detector) are considered to interact weakly with the beam and therefore produce fewer electrons. This is consistent with what is observed experimentally.

avec N(d) le niveau d'intensité d'un atome à la distance d du plan de projection, α et β dépendants du matériau et du protocole expérimental.The decay function can be of the following form: $$\mathrm{NOT}\left(d\right)=\alpha .d^{\beta }$$

with N(d) the intensity level of an atom at distance d from the projection plane, α and β depending on the material and the experimental protocol.

Thus, even in the presence of a sample modeled with a very large number of atoms 24, the atoms 24 furthest in depth (i.e. the atoms 24 furthest from the projection plane 21 representative of the atoms furthest from the source and of the detector) will play a weak role and will not saturate the projection.

In practice for a given atom 24, the definition of its theoretical interaction level results in the attribution of a gray level “N” to the atom. This gray level can be calculated using the aforementioned decay function or by using a correspondence table or by implementing any type of correspondence known to those skilled in the art.

• la valeur de niveau de gris « 255 » (correspondant au blanc) peut être attribuée aux atomes 24 de la structure contenus dans un volume compris entre le plan de projection 21 et le premier plan,
• la valeur de niveau de gris « 127 » (correspondant au gris) peut être attribuée aux atomes 24 de la structure contenus dans un volume compris entre les premiers et deuxième plans,
• la valeur de niveau de gris « 0 » (correspondant au noir) peut être attribuée aux autres atomes 24 de la structure (i.e. atomes situés au-delà du deuxième plan relativement au plan de projection).

For example, if we consider first and second planes parallel to the projection plane 21 and positioned at successively increasing distances from the projection plane 21 so that the first plane is closer to the projection plane 21 than the second plane, then :

• the gray level value “255” (corresponding to white) can be attributed to the atoms 24 of the structure contained in a volume between the projection plane 21 and the foreground,
• the gray level value “127” (corresponding to gray) can be attributed to the atoms 24 of the structure contained in a volume between the first and second planes,
• the gray level value “0” (corresponding to black) can be assigned to the other atoms 24 of the structure (ie atoms located beyond the second plane relative to the projection plane).

3.3. Projection

Another phase of the process consists of projecting the atoms 24 of the structure into the projection plane 21. The projection plane 21 corresponds to the plane in which the detector is contained.

When the spheres are projected onto the projection plane 21, they form discs each having an intensity level calculated as a function of the distance of the sphere from the projection plane 21 during the phase of defining the intensity levels. interaction.

This level of interaction can be visualized in the form of a gray level, the strongest interaction being represented in white (value 255) and the least strong in black (0) if the pixels of the projection plane 21 are assumed initialized to 0 (black).

However, the atoms 24 of the structure located in depth (i.e. the atoms 24 furthest from the projection plane 21) only interact with the beam if the latter has not already interacted with an atom 24 located above him in relation to the projection plane 21. It is therefore preferable to manage the “visibility” of the atoms by the beam during the projection.

For each atom 24, the projection is therefore carried out by displaying only the part of the atom 24 which is not masked by one or more atoms 24 located between it and the projection plane 21 in the direction of projection 23.

Different projection techniques can be used to take this projection criterion into account.

For example, all the atoms 24 can be projected onto the projection plane of the atom 24 from the furthest to the closest to the projection plane, the value assigned to each pixel of the projection plane being systematically replaced by the value associated with the projection plane. the atom 24 closest to the projection plane according to the projection direction 23.

3.4. Assessment

The projection can be viewed as a grayscale image, with atoms 24 having strong interaction with the beam being white and those having weaker interaction darker in color. We illustrated at figure 5 such an image.

Each visible portion of the projection of each atom 24 contributes up to its level of interaction and the projected visible surface to the final theoretical intensity. This can be interpreted graphically as a function of the total “brightness” of the projection viewed as a grayscale image.

The final intensity is calculated based on the sum of the values of all the pixels in the image. More precisely, the final intensity is for example calculated using a polynomial function, such as the square of the average of the values. The intensity thus calculated for a given acquisition geometry is reported in a graph representing the theoretical intensity as a function of the acquisition geometry.

To obtain a theoretical signature, we repeat the phases of definition of the levels of theoretical interaction with the beam of charged particles, projection, and evaluation for a plurality of different acquisition geometries. This results in a modification of the position of the projection plane relative to the modeling implemented during the modeling stage.

3.5. Improvements to the evaluation phase

The projection of the spherical model forms a disk whose outer edge is formed of a fairly small thickness of atoms 24. This does not pose a problem because the thickness of the sample is of the same distribution whatever the geometry of the sample. acquisition studied.

It is however possible to use only part of the projection image (obtained during the projection phase in the projection plane) while maintaining a good approximation of the expected intensity in order to limit the computational load during the computer implementation of the method.

• le carré inscrit : l'évaluation des contributions ne se fait que pour les éléments de projection situés dans un carré inscrit dans le disque de projection ; les résultats obtenus sont très proches étant donnée la faible pertinence des projetés en bordure de disque et permettent une économie de traitement significative ;
• l'élément unitaire de pavage : il est possible de calculer la projection d'une (ou plusieurs) maille(s) formant un pavage de l'espace dans l'image finale ; cela consiste à ne retenir comme zone d'analyse que l'enveloppe convexe de la projection de cette (ou ces) maille(s) ; dans le cas du TiN, il s'agit du projeté d'un cube ; cette projection représente une approximation d'un pavé sur le plan de projection et suffit à déduire une intensité théorique de bonne qualité ; le coût de calcul de l'enveloppe convexe est moindre que l'économie réalisée en surface d'analyse, l'optimisation est donc rentable.
• Approximation du pavé unitaire : plutôt que de réduire l'espace d'analyse à un pavé unitaire, on peut la réduire au carré dans lequel s'inscrit le pavé unitaire ; cette réduction ne dégrade que faiblement la qualité des intensités estimées et permet de s'affranchir du calcul de l'enveloppe convexe de projection.

With this in mind, three reduction methods set out below were studied:

• the inscribed square: the evaluation of the contributions is only done for the projection elements located in a square inscribed in the projection disk; the results obtained are very close given the low relevance of the projections at the edge of the disk and allow significant processing savings;
• the unitary tiling element: it is possible to calculate the projection of one (or more) mesh(es) forming a tiling of the space in the final image; this consists of retaining as the analysis zone only the convex envelope of the projection of this (or these) mesh(es); in the case of TiN, it is the projection of a cube; this projection represents an approximation of a block on the projection plane and is sufficient to deduce a theoretical intensity of good quality; the cost of calculating the convex hull is less than the saving made in analysis surface, the optimization is therefore profitable.
• Approximation of the unit block: rather than reducing the analysis space to a unit block, we can reduce it to the square in which the unit block fits; this reduction only slightly degrades the quality of the estimated intensities and makes it possible to dispense with the calculation of the convex projection envelope.

In order to limit processing times, we note that it is possible to exclude from the projection calculation the atoms 24 whose projected center is more than one atomic radius away from the area analyzed on the projection plane. , Which immediately allows us not to worry about the disks and the overlaps of the atoms 24 which will not have an impact on the result.

4. System for implementing the method for generating theoretical signatures

• des moyens de saisie - tels qu'un clavier ou une souris - pour permettre à un utilisateur le positionnement des atomes 24 d'une maille cristalline lors de la phase de modélisation,
• des moyens d'affichage - tels qu'un écran - pour permettre la visualisation des images de projection ou de la signature théorique, et
• des moyens de traitement - tels qu'un processeur ou un calculateur ou un microcontrôleur ou tout autre circuit programmable - pour estimer les signatures théoriques.

The method for generating theoretical signatures can be implemented in a processing system including:

• input means - such as a keyboard or a mouse - to allow a user to position the atoms 24 of a crystal mesh during the modeling phase,
• display means - such as a screen - to allow the visualization of the projection images or the theoretical signature, and
• processing means - such as a processor or a calculator or a microcontroller or any other programmable circuit - to estimate the theoretical signatures.

The processing system is for example computer(s), microcomputer(s), or other devices known to those skilled in the art such as a workstation.

The processing means are preferably coupled to one (or more) memory(s) which can be integrated into or separated from the processing means. The memory can be ROM/RAM memory, a USB key, memory from a central server. This memory makes it possible to store a computer program product comprising programming code instructions intended to execute the steps of the theoretical signature generation method according to claims 1 to 7.

5. Conclusions

A method and a computer program product have been described for generating theoretical signatures that can be used to map the crystal orientations of a material to be analyzed.

• Modéliser la structure atomique de l'échantillon de matériau selon une forme sphérique,
• Pour chaque point de la signature théorique :
  • ∘ Positionner la structure sphérique selon la géométrie d'acquisition désirée en déplaçant la structure sphérique par rapport au plan de projection, et définir la contribution de chaque atome 24 de la structure sphérique
  • ∘ Calculer la projection des atomes 24 contribuant au résultat,
  • ∘ Evaluer le résultat en fonction de la projection obtenue.

The process includes in particular the following phases:

• Model the atomic structure of the material sample in a spherical shape,
• For each point of the theoretical signature:
  • ∘ Position the spherical structure according to the desired acquisition geometry by moving the spherical structure relative to the projection plane, and define the contribution of each atom 24 of the spherical structure
  • ∘ Calculate the projection of the 24 atoms contributing to the result,
  • ∘ Evaluate the result based on the projection obtained.

Unlike previous theoretical signature calculation methods, the method according to the invention takes into account physical phenomena to overcome the calculation errors of previous methods.

In particular, by weighting each atom 24 by a coefficient representative of its visibility, the method according to the invention takes into account the fact that the penetration depth of the beam of charged particles is limited to a maximum thickness of the material analyzed.

Furthermore, by creating a crystal structure of interest whose atoms 24 located at the periphery are inscribed in a volume having a central symmetry of revolution, the process makes it possible to overcome undesirable edge effects linked to the rotation of the structure.

• le rayonnement rétrodiffusé ayant été reçu par le détecteur
• du rayonnement rétrodiffusé ayant été bloqué par un atome 24 situé sur le chemin de parcours dudit rayonnement rétrodiffusé.

Finally, by retaining in the projection only the portions of atoms not covered by an atom 24 located at a lower distance from the projection plane, the method according to the invention makes it possible to distinguish:

• the backscattered radiation having been received by the detector
• backscattered radiation having been blocked by an atom 24 located on the path of said backscattered radiation.

We avoid the risks of accumulation of contributions between the atoms 24 at different depths.

The method described above was evaluated on samples of titanium and iron nitride, with a cubic crystal structure, but can be generalized to other crystal structures. In particular, the method described above can be used to generate theoretical signatures for any type of polycrystalline material such as a metal or a ceramic.

The reader will have understood that numerous modifications can be made to the process described above without materially departing from the new teachings presented here.

For example, the method can be used to determine the theoretical signatures of a single crystal material.

It is therefore quite obvious that the examples which have just been given are only illustrations and in no way limiting.

Claims (8)

1. A method for creating a theoretical signature of a crystalline material sample, the theoretical signature corresponding to a curve of theoretical backscattered intensities as a function of acquisition geometries, characterised in that the method comprises the following steps:

   - modelling (10) a three-dimensional atomic structure of the sample, the structure comprising at least one crystal lattice, said modelling step comprising a sub-step consisting of selecting atoms (24) of at least one crystal lattice and contained in a selection volume, the selection volume having a symmetry of rotation such that the distance between a centre of the structure and the atoms (24) arranged at the periphery of the structure is substantially constant;

   - then, for each acquisition geometry:

   ∘ positioning (20) the structure according to the desired acquisition geometry by moving the spherical structure relative to the projection plane;

   ∘ defining (30) a level of interaction for each atom, said step consisting of allocating, to each atom, a coefficient representative of a theoretical contribution of the atom to the backscattered intensity, said coefficient consisting of a greyscale value attributed to each atom of the structure according as a function of:

   ▪ the distance between said given atom and the projection plane, and/or

   ▪ the number of atoms located between said given atom and the projection plane,

   ∘ calculating (40) the projection of the atoms (24) of the structure in the projection plane in order to obtain a projection image;

   ∘ estimating (50) the backscattered intensity on the basis of the projection image; and

   - generating the theoretical signature on the basis of a plurality of estimated theoretical backscattered intensities.
2. The method according to claim 1, wherein the three-dimensional structure is spherical.
3. The method according to either of claims 1 or 2, wherein the definition step (30) consists, for a given atom of the structure, in attributing a greyscale value to each atom as a function of the distance to said given atom, the attributed greyscale value being calculated on the basis of a decay function of the following form: $$N\left(d\right)=\alpha .d^{\beta }$$

   

   where:

   - N(d): the greyscale to be attributed to the atom

   - d : the distance between the atom and the projection plane,

   - α and β are fixed coefficients.
4. The method according to any one of claims 1 to 3, wherein the step of calculating the projection comprises attributing to each pixel of the projection image:

   - the value 0 if no atom is crossed by the projection direction (23),

   - the value associated with the atom closest to the projection plane (21) if at least one atom is crossed by the projection direction (23).
5. The method according to any one of claims 1 to 4, wherein the step of estimating the intensity comprises the application of a polynomial function to the greyscale values of the pixels of the projection image.
6. The method according to any one of claims 1 to 4, wherein the step of estimating the intensity comprises the sub-steps consisting of:

   - selecting a region of the projection image,

   - summing the greyscale values of the pixels of the selected region, and

   - dividing the sum obtained by the number of pixels of the selected region.
7. The method according to any one of the preceding claims, wherein the modelling step comprises the sub-steps consisting of:

   - producing the crystal lattice, in particular on the basis of a three-dimensional modelling software,

   - repeating the crystal lattice in at least one (in particular each) of the three spatial dimensions in order to generate a three-dimensional crystal skeleton,

   - forming the three-dimensional atomic structure on the basis of the three-dimensional crystal skeleton.
8. A computer program product comprising program code instructions for executing the steps of the method according to any one of claims 1 to 7 when said program is executed on a computer.

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